What drives antigenic drift in a single influenza season
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What drives antigenic drift in a single influenza season?. Maciej F. Boni Stanford University, Department of Biological Sciences Co-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman. DIMACS Workshop on the Epidemiology and Evolution of Influenza Rutgers University, January 26, 2006.

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What drives antigenic drift in a single influenza season?

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What drives antigenic drift in a single influenza season?

Maciej F. BoniStanford University, Department of Biological SciencesCo-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman

DIMACS Workshop on the Epidemiology and Evolution of Influenza

Rutgers University, January 26, 2006


Strains have accumulated mutations. But how many?

epidemic strain

NOV

APR

Flu epidemics and antigenic drift

weekly illnesses/10,000 inhabitants (NL)

20

( focus will be on HA1 )

1996

1997

1998

de Jong et al (2000)


HA1 polymorphism – local datasets

  • Coiras et al, Arch. Vir. (2001)

  • Schweiger et al, Med. Microbiol. Immunol. (2002)

  • Pyhälä et al, J. Med. Virol. (2004)

mean within-season distance = 2.8 aa (6nt)

max within-season distance = 8 aa (25nt)


Number of infections with epidemic-originating strain

Number of infections with a strain k mutations away

Neutral Epidemic Model


Exiting a population class via mutation

Neutral Epidemic Model


Strain frequencies are Poisson-distributed

Frequency of strain k:

Mean number of mutations per virus moves forward in time

according to a “molecular clock.”


you may have conferred immunity from a previous season to one of these strains.

Modeling antigenic drift and immunity

the epidemic-originating strain

-2

-1

0

1

2

3

4


Modeling antigenic drift and immunity

the epidemic-originating strain

-2

-1

0

1

2

3

4

Distance between immunizing strain and challenging strain determines level of cross-immunity.

We model this as an infectivity reduction and say it wanes exponentially with distance:


Non-neutral model

  • Amino-acid replacements in influenza surface proteins confer a fitness benefit via increased transmissibility

  • Hosts have some immunity structure from vaccination or previous infections

    ( need both )


j+kis distance between immunizing and challenging (infecting) strain

Keeping track of hosts


infectivity reduction by previous infection

with a strain j amino acids away

force of infection of strain k

total force of infection

Keeping track of variables


Equations


total immunity in population

cross-immunity between strains mamino acids apart

Equations


mean fitness of strain population: W

Equations

fitness of strain k


Fisher’s Fundamental Theorem

Population genetics

Define mean antigenic drift in virus population as:

This is the Price Equation, thus, the basic influenza population dynamics

can be viewed in a standard population genetic framework.


Under neutrality


Takes 7 aa-changes to escape 50% immunity

I(t)


Define the excess antigenic drift as:

How do you know when the epidemic ends?


I(t)


In general, how do the parameters affect the model results?


Partial correlations

immunity :

immune-escape/mutation :


Partial correlations

immunity :

immune-escape/mutation :


Host immunity drives antigenic drift


Public health implications

  • Vaccination strategies: under-vaccination or imperfect vaccination may cause much excess antigenic drift.

  • Pandemic implications: need to consider the effects of vaccination during the 2nd year after a pandemic, and their effects on the 3rd year after a pandemic.


Thanks

Viggo Andreasen

University of Roskile, Department of Mathematics and Physics

Julia Gog

Cambridge University, Department of Zoology

Marc Feldman

Stanford University, Department of Biological Sciences

Freddy Christiansen

University of Aarhus, Department of Biology

Mike Macpherson

Stanford University, Department of Biological Sciences

( and for funding to NIH grant GM28016, NSF, and Stanford University )


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